Question

What is the definition of a localization of a category?

score 271 · Answer 1 · 2026-03-22 09:14:57

271

Views

What is the definition of a localization of a category?

Published on 22 Mar 2026 - 9:14

score 47 · Answer 2 · 2018-10-08 02:54:53

47

Views

Naturality of Conditional Expectation

Published on 08 Oct 2018 - 2:54

score 54 · Answer 3 · 2018-10-21 14:52:36

54

Views

The category of functors if the codomain category has zero object is non-empty. Why?

Published on 21 Oct 2018 - 14:52

score 38 · Answer 4 · 2018-10-23 00:26:02

38

Views

How to prove naturality in $c$ of $\text{Hom}_D(Fc, d) \simeq \text{Hom}_C(c, Ud)$ given adjunction $(F, U)$?

Published on 23 Oct 2018 - 0:26

score 138 · Answer 5 · 2018-10-29 11:20:18

138

Views

Does the functor $V\mapsto V^{**}/V$ (for $\dim V=\infty$) reflect monomorphisms, epimorphisms or isomorphisms?

Published on 29 Oct 2018 - 11:20

score 102 · Answer 6 · 2018-10-30 05:50:09

102

Views

In the proof of the Yoneda Lemma in "Categories & Sheaves" by Kashiwara & Schapira.

Published on 30 Oct 2018 - 5:50

score 60 · Answer 7 · 2018-10-30 05:56:14

60

Views

If $F$ and $G$ are adjoint functors, why are $\operatorname{Nat}(G,G)\simeq\operatorname{Nat}(F,F)$ as algebras?

Published on 30 Oct 2018 - 5:56

score 41 · Answer 8 · 2026-03-17 20:53:11

41

Views

How do you arrive at $\eta : \text{Hom}_{C'}(Y, Y') \to \text{Hom}_{C'}(LR(Y), Y')$ from $\eta : LR \to \text{id}_{C'}$?

Published on 17 Mar 2026 - 20:53

score 173 · Answer 9 · 2018-10-30 18:13:07

173

Views

An exercise about bifunctors from Riehl's "Category Theory in Context"

Published on 30 Oct 2018 - 18:13

score 88 · Answer 10 · 2018-10-31 10:44:11

88

Views

A bijection $\mathsf{Ob}([\mathsf{C\times D},\mathsf{E}])\to\mathsf{Ob}([\mathsf{C},[\mathsf{D},\mathsf{E}]])$

Published on 31 Oct 2018 - 10:44

score 111 · Answer 11 · 2026-03-22 04:46:16

111

Views

Nearly locally presentable categories

Published on 22 Mar 2026 - 4:46

score 79 · Answer 12 · 2018-11-16 17:04:05

79

Views

Right whiskering, unknown naturality

Published on 16 Nov 2018 - 17:04

score 77 · Answer 13 · 2026-03-16 21:40:26

77

Views

Proving for two naturally isomorphic functors, if one is full, then so is the other.

Published on 16 Mar 2026 - 21:40

score 364 · Answer 14 · 2026-03-17 10:34:02

364

Views

Showing when two functors are naturally isomorphic, if one is faithful, then the other also is.

Published on 17 Mar 2026 - 10:34

score 2.3k · Answer 15 · 2018-11-20 14:25:51

2.3k

Views

Definition of symmetric power of a linear represenation

Published on 20 Nov 2018 - 14:25

List Question

What is the definition of a localization of a category?

Naturality of Conditional Expectation

The category of functors if the codomain category has zero object is non-empty. Why?

How to prove naturality in $c$ of $\text{Hom}_D(Fc, d) \simeq \text{Hom}_C(c, Ud)$ given adjunction $(F, U)$?

Does the functor $V\mapsto V^{**}/V$ (for $\dim V=\infty$) reflect monomorphisms, epimorphisms or isomorphisms?

In the proof of the Yoneda Lemma in "Categories & Sheaves" by Kashiwara & Schapira.

If $F$ and $G$ are adjoint functors, why are $\operatorname{Nat}(G,G)\simeq\operatorname{Nat}(F,F)$ as algebras?

How do you arrive at $\eta : \text{Hom}_{C'}(Y, Y') \to \text{Hom}_{C'}(LR(Y), Y')$ from $\eta : LR \to \text{id}_{C'}$?

An exercise about bifunctors from Riehl's "Category Theory in Context"

A bijection $\mathsf{Ob}([\mathsf{C\times D},\mathsf{E}])\to\mathsf{Ob}([\mathsf{C},[\mathsf{D},\mathsf{E}]])$

Nearly locally presentable categories

Right whiskering, unknown naturality

Proving for two naturally isomorphic functors, if one is full, then so is the other.

Showing when two functors are naturally isomorphic, if one is faithful, then the other also is.

Definition of symmetric power of a linear represenation

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